I was wondering if there was a really good place to learn about this topic that actually contains the details of the construction from beginning to end. I'm familiar with the book by Harris and Morrison, and many of the papers about the construction. The recent book by Arbarello, Cornalba, and Griffiths covers the complex case in a very nice and detailed way, but I was wondering if there was a good place to learn this 1) that only uses algebraic geometry and not complex analytic geometry, and 2) that covers the construction over $\mathbb Z$ so one can use it in the arithmetic case. Most books simply leave so many details out that a beginner in the subject finds it hard to fill them all in and truly understand the construction. Any good references would be much appreciated. Thanks
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These notes by Dan Edidin: http://www.math.missouri.edu/~edidin/Papers/mfile.pdf give a very readable account of the construction of the moduli stack of curves over $\mathrm{Spec}(\mathbb Z)$ for $g \geq 3$ via the Hilbert scheme. I am not sure if this is what you are looking for, though, depending on what you mean with "from beginning to end": certainly there are several steps left as pointers to the literature. 

